Rewrite as a simplified fraction. ${3.4\overline{17} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3417.1717...\\ 10x &= 34.1717...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3383}$ ${x = \dfrac{3383}{990}} \text{or} {3 \dfrac{413}{990}}$